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This article discusses the notion of convergence of sequences of iteratedfunction systems. The technique of iterated function systems is one of theseveral methods to construct objects with fractal nature, and the fractalsobtained with this method are mostly self-similar. The progress in the theoryof fractals has found potential applications in the fields of physical science,computer science, and economics in abundance. This paper considers the metricspace of $n$- iterated function systems by introducing a metric function on theset of all iterated function systems on a complete metric space consisting of$n$ contraction functions. Further, sequences of $n$- iterated function systemswith decreasing, eventually decreasing, Cauchy and convergent properties arediscussed. Some results on sequences of $n$- iterated function systems andsequences of contractions are obtained. The practical usage of the theorydiscussed in the article is explored towards the end.

On the convergence of sequences in the space of $n$-iterated function systems with applications